Solve 21/2+62^2+3^2-44^2

$$2 \frac{ 1 }{ 2 } +6 { 2 }^{ 2 } + { 3 }^{ 2 } - { 44 }^{ 2 }$$

Evaluate

$$-\frac{3801}{2}=-1900.5$$

Solution Steps

Multiply 2 and 2 to get 4.

$$\frac{4+1}{2}+6\times 2^{2}+3^{2}-44^{2}$$

Add 4 and 1 to get 5.

$$\frac{5}{2}+6\times 2^{2}+3^{2}-44^{2}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{5}{2}+6\times 4+3^{2}-44^{2}$$

Multiply 6 and 4 to get 24.

$$\frac{5}{2}+24+3^{2}-44^{2}$$

Convert 24 to fraction \frac{48}{2}.

$$\frac{5}{2}+\frac{48}{2}+3^{2}-44^{2}$$

Since \frac{5}{2} and \frac{48}{2} have the same denominator, add them by adding their numerators.

$$\frac{5+48}{2}+3^{2}-44^{2}$$

Add 5 and 48 to get 53.

$$\frac{53}{2}+3^{2}-44^{2}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{53}{2}+9-44^{2}$$

Convert 9 to fraction \frac{18}{2}.

$$\frac{53}{2}+\frac{18}{2}-44^{2}$$

Since \frac{53}{2} and \frac{18}{2} have the same denominator, add them by adding their numerators.

$$\frac{53+18}{2}-44^{2}$$

Add 53 and 18 to get 71.

$$\frac{71}{2}-44^{2}$$

Calculate 44 to the power of 2 and get 1936.

$$\frac{71}{2}-1936$$

Convert 1936 to fraction \frac{3872}{2}.

$$\frac{71}{2}-\frac{3872}{2}$$

Since \frac{71}{2} and \frac{3872}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{71-3872}{2}$$

Subtract 3872 from 71 to get -3801.

$$-\frac{3801}{2}$$

Factor

$$-\frac{3801}{2} = -1900\frac{1}{2} = -1900.5$$